Leibniz algebras in which all centralisers of nonzero elements are zero algebras

This paper is concerned with generalising the results for Lie CT-algebras to Leibniz algebras. In some cases our results give a generalisation even for the case of a Lie algebra. Results on A-algebras are used to show every Leibniz CT-algebra over an algebraically closed field of characteristic different from 2, 3 is solvable or is isomorphic to sl₂ (F). A characterisation is then given for solvable Leibniz CT-algebras. It is also shown that the class of solvable Leibniz CT-algebras is factor closed.